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Moutard Transform for Generalized Analytic Functions

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Abstract

We construct a Moutard-type transform for generalized analytic functions. The first theorems and the first explicit examples in this connection are given.

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Acknowledgments

The main part of the work was fulfilled during the visit of the first author to the Centre de Mathématiques Appliquées of École Polytechnique in October 2015. The first author was partially supported by the Russian Foundation for Basic Research, Grant 13-01-12469 ofi-m2, by the Program “Leading scientific schools” (Grant NSh-4833.2014.1), by the Program “Fundamental problems of nonlinear dynamics”.

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Correspondence to R. G. Novikov.

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Grinevich, P.G., Novikov, R.G. Moutard Transform for Generalized Analytic Functions. J Geom Anal 26, 2984–2995 (2016). https://doi.org/10.1007/s12220-015-9657-8

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  • DOI: https://doi.org/10.1007/s12220-015-9657-8

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